OpenRaiser/Intern-Atlas huggingface dataset:
Practical design of multi-channel oversampled warped cosine-modulated filter banks
Venue: arXiv cs.IT 2020
Year: 2020

A practical approach to optimal design of multichannel oversampled warped cosine-modulated filter banks (CMFB) is proposed. Warped CMFB is obtained by allpass transformation of uniform CMFB. The paper addresses the problems of minimization amplitude distortion and suppression of aliasing components emerged due to oversampling of filter bank channel signals. Proposed optimization-based design considerably reduces distortions of overall filter bank transfer function taking into account channel subsampling ratios. Matlab-implementation of the proposed warped CMFB design method is available in public GitHub repository.
Paraunitary Matrices
Venue: arXiv cs.IT 2020
Year: 2020

Design methods for paraunitary matrices from complete orthogonal sets of idempotents and related matrix structures are presented. These include techniques for designing non-separable multidimensional paraunitary matrices. Properties of the structures are obtained and proofs given. Paraunitary matrices play a central role in signal processing, in particular in the areas of filterbanks and wavelets.
Comparative Study and Optimization of Feature-Extraction Techniques for Content based Image Retrieval
Venue: arXiv cs.CV 2020
Year: 2020

The aim of a Content-Based Image Retrieval (CBIR) system, also known as Query by Image Content (QBIC), is to help users to retrieve relevant images based on their contents. CBIR technologies provide a method to find images in large databases by using unique descriptors from a trained image. The image descriptors include texture, color, intensity and shape of the object inside an image. Several feature-extraction techniques viz., Average RGB, Color Moments, Co-occurrence, Local Color Histogram, Global Color Histogram and Geometric Moment have been critically compared in this paper. However, individually these techniques result in poor performance. So, combinations of these techniques have also been evaluated and results for the most efficient combination of techniques have been presented and optimized for each class of image query. We also propose an improvement in image retrieval performance by introducing the idea of Query modification through image cropping. It enables the user to identify a region of interest and modify the initial query to refine and personalize the image retrieval results.
Approximation Algorithms for the Load Balanced Capacitated Vehicle Routing Problem
Venue: arXiv cs.DS 2020
Year: 2020

We study the load balanced capacitated vehicle routing problem (LBCVRP): the problem is to design a collection of tours for a fixed fleet of vehicles with capacity Q to distribute a supply from a single depot between a number of predefined clients, in a way that the total traveling cost is a minimum, and the vehicle loads are balanced. The unbalanced loads cause the decrease of distribution quality especially in business environments and exibility in the logistics activities. The problem being NP-hard, we propose two approximation algorithms. When the demands are equal, we present a (1-1/Q)p+3/2approximation algorithm that finds balanced loads. Here, p is the approximation ratio for the known metric traveling salesman problem (TSP). This result leads to a 2.5-1/Q approximation ratio for the tree metrics since an optimal solution can be found for the TSP on a tree. We present an improved 2 approximation algorithm. When the demands are unequal, we focus on obtaining approximate solutions since finding balanced loads is NP-complete. We propose an algorithm that provides a 4 approximation for the balance of the loads. We assume a second approach to get around the difficulties of the feasibility. In this approach, we redefine and convert the problem into a multi-objective problem. The algorithm we propose has a 4 factor of approximation.
Computing the multilinear factors of lacunary polynomials without heights
Venue: arXiv cs.SC 2020
Year: 2020

We present a deterministic algorithm which computes the multilinear factors of multivariate lacunary polynomials over number fields. Its complexity is polynomial in $\ell^n$ where $\ell$ is the lacunary size of the input polynomial and $n$ its number of variables, that is in particular polynomial in the logarithm of its degree. We also provide a randomized algorithm for the same problem of complexity polynomial in $\ell$ and $n$. Over other fields of characteristic zero and finite fields of large characteristic, our algorithms compute the multilinear factors having at least three monomials of multivariate polynomials. Lower bounds are provided to explain the limitations of our algorithm. As a by-product, we also design polynomial-time deterministic polynomial identity tests for families of polynomials which were not known to admit any. Our results are based on so-called Gap Theorem which reduce high-degree factorization to repeated low-degree factorizations. While previous algorithms used Gap Theorems expressed in terms of the heights of the coefficients, our Gap Theorems only depend on the exponents of the polynomials. This makes our algorithms more elementary and general, and faster in most cases.
Extensions of the I-MMSE Relationship to Gaussian Channels with Feedback and Memory
Venue: arXiv cs.IT 2020
Year: 2020

Unveiling a fundamental link between information theory and estimation theory, the I-MMSE relationship by Guo, Shamai and Verdu~\cite{gu05}, together with its numerous extensions, has great theoretical significance and various practical applications. On the other hand, its influences to date have been restricted to channels without feedback or memory, due to the absence of its extensions to such channels. In this paper, we propose extensions of the I-MMSE relationship to discrete-time and continuous-time Gaussian channels with feedback and/or memory. Our approach is based on a very simple observation, which can be applied to other scenarios, such as a simple and direct proof of the classical de Bruijn's identity. This submission corrects the mistakes in the previous version.
Nondeterministic automatic complexity of overlap-free and almost square-free words
Venue: arXiv cs.FL 2020
Year: 2020

Shallit and Wang studied deterministic automatic complexity of words. They showed that the automatic Hausdorff dimension $I(\mathbf t)$ of the infinite Thue word satisfies $1/3\le I(\mathbf t)\le 2/3$. We improve that result by showing that $I(\mathbf t)\ge 1/2$. For nondeterministic automatic complexity we show $I(\mathbf t)=1/2$. We prove that such complexity $A_N$ of a word $x$ of length $n$ satisfies $A_N(x)\le b(n):=\lfloor n/2\rfloor + 1$. This enables us to define the complexity deficiency $D(x)=b(n)-A_N(x)$. If $x$ is square-free then $D(x)=0$. If $x$ almost square-free in the sense of Fraenkel and Simpson, or if $x$ is a strongly cube-free binary word such as the infinite Thue word, then $D(x)\le 1$. On the other hand, there is no constant upper bound on $D$ for strongly cube-free words in a ternary alphabet, nor for cube-free words in a binary alphabet. The decision problem whether $D(x)\ge d$ for given $x$, $d$ belongs to $NP\cap E$.
A Simple and Approximately Optimal Mechanism for an Additive Buyer
Venue: arXiv cs.GT 2020
Year: 2020

We consider a monopolist seller with $n$ heterogeneous items, facing a single buyer. The buyer has a value for each item drawn independently according to (non-identical) distributions, and her value for a set of items is additive. The seller aims to maximize his revenue. We suggest using the a-priori better of two simple pricing methods: selling the items separately, each at its optimal price, and bundling together, in which the entire set of items is sold as one bundle at its optimal price. We show that for any distribution, this mechanism achieves a constant-factor approximation to the optimal revenue. Beyond its simplicity, this is the first computationally tractable mechanism to obtain a constant-factor approximation for this multi-parameter problem. We additionally discuss extensions to multiple buyers and to valuations that are correlated across items.
BSROne: Binary Search with Routing of O(1); A Scalable Circular Design for Distributed Networks
Venue: arXiv cs.NI 2020
Year: 2020

Peer-to-Peer (P2P) networks as distributed solutions are used in a variety of applications. Based on the type of routing for queries among their nodes, they are classified into three groups: structured, unstructured and small-world P2P networks. Each of these categories has its own applications and benefits. Structured networks by using Distributed Hash Tables (DHT) can forward request search queries more efficiently. These networks usually organize a specific topology and make a geometrical shape. A circular topology is a prevalent design which was first introduced by Chord. In this paper, we propose BSROne, a circular structured P2P design which attempts to consider several shortcomings in the current networks. In our proposed method, we want to achieve O(1) routing time without requiring all of the nodes to know about each other. By removing the real connections between nodes and tying all of them with super-nodes, we could reduce the number of overheads that are essential to maintain the connectivity between nodes in such networks. Furthermore, we gave the network an ability to scale up by introducing one layer above super-nodes. We achieved this by emulating the design of binary search algorithm for supreme-nodes. In this paper, at first we introduce a design where fixed super-nodes with unlimited resources are given to the distributed network. In the next step, we explain how it can manage to work as a P2P application. We finally discuss the possibility of removing the scalability issue in a P2P environment for our design.
Scheduling with Gaps: New Models and Algorithms
Venue: arXiv cs.DS 2020
Year: 2020

We consider scheduling problems for unit jobs with release times, where the number or size of the gaps in the schedule is taken into consideration, either in the objective function or as a constraint. Except for a few papers on energy minimization, there is no work in the scheduling literature that uses performance metrics depending on the gap structure of a schedule. One of our objectives is to initiate the study of such scheduling problems with gaps. We show that such problems often lead to interesting algorithmic problems, with connections to other areas of algorithmics. We focus on the model with unit jobs. First we examine scheduling problems with deadlines, where we consider variants of minimum-gap scheduling, including maximizing throughput with a budget for gaps or minimizing the number of gaps with a throughput requirement. We then turn to other objective functions. For example, in some scenarios, gaps in a schedule may be actually desirable, leading to the problem of maximizing the number of gaps. Other versions we study include minimizing maximum gap or maximizing minimum gap. The second part of the paper examines the model without deadlines, where we focus on the tradeoff between the number of gaps and the total or maximum flow time. For all these problems we provide polynomial time algorithms, with running times ranging from $O(n \log n)$ for some problems, to $O(n^7)$ for other. The solutions involve a spectrum of algorithmic techniques, including different dynamic programming formulations, speed-up techniques based on searching Monge arrays, searching X + Y matrices, or implicit binary search.
Optimal Hierarchical Radio Resource Management for HetNets with Flexible Backhaul
Venue: arXiv cs.IT 2020
Year: 2020

Providing backhaul connectivity for macro and pico base stations (BSs) constitutes a significant share of infrastructure costs in future heterogeneous networks (HetNets). To address this issue, the emerging idea of flexible backhaul is proposed. Under this architecture, not all the pico BSs are connected to the backhaul, resulting in a significant reduction in the infrastructure costs. In this regard, pico BSs without backhaul connectivity need to communicate with their nearby BSs in order to have indirect accessibility to the backhaul. This makes the radio resource management (RRM) in such networks more complex and challenging. In this paper, we address the problem of cross-layer RRM in HetNets with flexible backhaul. We formulate this problem as a two-timescale non-convex stochastic optimization which jointly optimizes flow control, routing, interference mitigation and link scheduling in order to maximize a generic network utility. By exploiting a hidden convexity of this non-convex problem, we propose an iterative algorithm which converges to the global optimal solution. The proposed algorithm benefits from low complexity and low signalling, which makes it scalable. Moreover, due to the proposed two-timescale design, it is robust to the backhaul signalling latency as well. Simulation results demonstrate the significant performance gain of the proposed solution over various baselines.
Approximation Algorithms for the Connected Sensor Cover Problem
Venue: arXiv cs.DS 2020
Year: 2020

We study the minimum connected sensor cover problem (MIN-CSC) and the budgeted connected sensor cover (Budgeted-CSC) problem, both motivated by important applications (e.g., reduce the communication cost among sensors) in wireless sensor networks. In both problems, we are given a set of sensors and a set of target points in the Euclidean plane. In MIN-CSC, our goal is to find a set of sensors of minimum cardinality, such that all target points are covered, and all sensors can communicate with each other (i.e., the communication graph is connected). We obtain a constant factor approximation algorithm, assuming that the ratio between the sensor radius and communication radius is bounded. In Budgeted-CSC problem, our goal is to choose a set of $B$ sensors, such that the number of targets covered by the chosen sensors is maximized and the communication graph is connected. We also obtain a constant approximation under the same assumption.
Learning and Efficiency in Games with Dynamic Population
Venue: arXiv cs.GT 2020
Year: 2020

We study the quality of outcomes in repeated games when the population of players is dynamically changing and participants use learning algorithms to adapt to the changing environment. Game theory classically considers Nash equilibria of one-shot games, while in practice many games are played repeatedly, and in such games players often use algorithmic tools to learn to play in the given environment. Most previous work on learning in repeated games assumes that the population playing the game is static over time. We analyze the efficiency of repeated games in dynamically changing environments, motivated by application domains such as Internet ad-auctions and packet routing. We prove that, in many classes of games, if players choose their strategies in a way that guarantees low adaptive regret, then high social welfare is ensured, even under very frequent changes. In fact, in large markets learning players achieve asymptotically optimal social welfare despite high turnover. Previous work has only showed that high welfare is guaranteed for learning outcomes in static environments. Our work extends these results to more realistic settings when participation is drastically evolving over time.
Visualization of Tradeoff in Evaluation: from Precision-Recall & PN to LIFT, ROC & BIRD
Venue: arXiv cs.LG 2020
Year: 2020

Evaluation often aims to reduce the correctness or error characteristics of a system down to a single number, but that always involves trade-offs. Another way of dealing with this is to quote two numbers, such as Recall and Precision, or Sensitivity and Specificity. But it can also be useful to see more than this, and a graphical approach can explore sensitivity to cost, prevalence, bias, noise, parameters and hyper-parameters. Moreover, most techniques are implicitly based on two balanced classes, and our ability to visualize graphically is intrinsically two dimensional, but we often want to visualize in a multiclass context. We review the dichotomous approaches relating to Precision, Recall, and ROC as well as the related LIFT chart, exploring how they handle unbalanced and multiclass data, and deriving new probabilistic and information theoretic variants of LIFT that help deal with the issues associated with the handling of multiple and unbalanced classes.
Elementary Properties of Positive Concave Mappings with Applications to Network Planning and Optimization
Venue: arXiv cs.IT 2020
Year: 2020

This study presents novel methods for computing fixed points of positive concave mappings and for characterizing the existence of fixed points. These methods are particularly important in planning and optimization tasks in wireless networks. For example, previous studies have shown that the feasibility of a network design can be quickly evaluated by computing the fixed point of a concave mapping that is constructed based on many environmental and network control parameters such as the position of base stations, channel conditions, and antenna tilts. To address this and more general problems, given a positive concave mapping, we show two alternative but equivalent ways to construct a matrix that is guaranteed to have spectral radius strictly smaller than one if the mapping has a fixed point. This matrix is then used to build a new mapping that preserves the fixed point of the original positive concave mapping. We show that the standard fixed point iterations using the new mapping converges faster than the standard iterations applied to the original concave mapping. As exemplary applications of the proposed methods, we consider the problems of power and load planning in networks based on the orthogonal frequency division multiple access (OFDMA) technology.
Partial resampling to approximate covering integer programs
Venue: arXiv cs.DS 2020
Year: 2020

We consider column-sparse covering integer programs, a generalization of set cover, which have a long line of research of (randomized) approximation algorithms. We develop a new rounding scheme based on the Partial Resampling variant of the Lovász Local Lemma developed by Harris & Srinivasan (2019). This achieves an approximation ratio of $1 + \frac{\ln (Δ_1+1)}{a_{\min}} + O\Big( \log(1 + \sqrt{ \frac{\log (Δ_1+1)}{a_{\min}}} \Big)$, where $a_{\min}$ is the minimum covering constraint and $Δ_1$ is the maximum $\ell_1$-norm of any column of the covering matrix (whose entries are scaled to lie in $[0,1]$). When there are additional constraints on the variable sizes, we show an approximation ratio of $\ln Δ_0 + O(\log \log Δ_0)$ (where $Δ_0$ is the maximum number of non-zero entries in any column of the covering matrix). These results improve asymptotically, in several different ways, over results of Srinivasan (2006) and Kolliopoulos & Young (2005). We show nearly-matching inapproximability and integrality-gap lower bounds. We also show that the rounding process leads to negative correlation among the variables, which allows us to handle multi-criteria programs.
Computing Spectra -- On the Solvability Complexity Index Hierarchy and Towers of Algorithms
Venue: arXiv cs.CC 2020
Year: 2020

This paper establishes some of the fundamental barriers in the theory of computations and finally settles the long-standing computational spectral problem. That is to determine the existence of algorithms that can compute spectra $\mathrm{sp}(A)$ of classes of bounded operators $A = \{a_{ij}\}_{i,j \in \mathbb{N}} \in \mathcal{B}(l^2(\mathbb{N}))$, given the matrix elements $\{a_{ij}\}_{i,j \in \mathbb{N}}$, that are sharp in the sense that they achieve the boundary of what a digital computer can achieve. Similarly, for a Schrödinger operator $H = -Δ+V$, determine the existence of algorithms that can compute the spectrum $\mathrm{sp}(H)$ given point samples of the potential function $V$. In order to solve these problems, we establish the Solvability Complexity Index (SCI) hierarchy and provide a collection of new algorithms that allow for problems that were previously out of reach. The SCI is the smallest number of limits needed in the computation, yielding a classification hierarchy for all types of problems in computational mathematics that determines the boundaries of what computers can achieve in scientific computing. In addition, the SCI hierarchy provides classifications of computational problems that can be used in computer-assisted proofs. The SCI hierarchy captures many key computational issues in the history of mathematics including the insolvability of the quintic, Smale's problem on the existence of iterative generally convergent algorithm for polynomial root finding, the computational spectral problem, inverse problems, optimisation etc.
The Diagonal Lemma Fails in Aristotelian Logic
Venue: arXiv cs.LO 2020
Year: 2020

In the 1950-ies P. F. Strawson proposed the Logic of Presuppositions. In this system sentences with empty subject are considered neither true nor false. Strawson considered only simple sentences with two predicate letters. But the concept can be extended to arbitrary monadic, even polyadic sentences utilizing truth-relevant logic developed by Richard Diaz. It can be shown that self-referential Gödel's sentence in fact has an empty subject, and can thus be classified by the Logic of Presuppositions as neither true nor false.
Trace Refinement in Labelled Markov Decision Processes
Venue: arXiv cs.LO 2020
Year: 2020

Given two labelled Markov decision processes (MDPs), the trace-refinement problem asks whether for all strategies of the first MDP there exists a strategy of the second MDP such that the induced labelled Markov chains are trace-equivalent. We show that this problem is decidable in polynomial time if the second MDP is a Markov chain. The algorithm is based on new results on a particular notion of bisimulation between distributions over the states. However, we show that the general trace-refinement problem is undecidable, even if the first MDP is a Markov chain. Decidability of those problems was stated as open in 2008. We further study the decidability and complexity of the trace-refinement problem provided that the strategies are restricted to be memoryless.
An Action Language for Multi-Agent Domains: Foundations
Venue: arXiv cs.AI 2020
Year: 2020

In multi-agent domains (MADs), an agent's action may not just change the world and the agent's knowledge and beliefs about the world, but also may change other agents' knowledge and beliefs about the world and their knowledge and beliefs about other agents' knowledge and beliefs about the world. The goals of an agent in a multi-agent world may involve manipulating the knowledge and beliefs of other agents' and again, not just their knowledge/belief about the world, but also their knowledge about other agents' knowledge about the world. Our goal is to present an action language (mA+) that has the necessary features to address the above aspects in representing and RAC in MADs. mA+ allows the representation of and reasoning about different types of actions that an agent can perform in a domain where many other agents might be present -- such as world-altering actions, sensing actions, and announcement/communication actions. It also allows the specification of agents' dynamic awareness of action occurrences which has future implications on what agents' know about the world and other agents' knowledge about the world. mA+ considers three different types of awareness: full-, partial- awareness, and complete oblivion of an action occurrence and its effects. This keeps the language simple, yet powerful enough to address a large variety of knowledge manipulation scenarios in MADs. The semantics of mA+ relies on the notion of state, which is described by a pointed Kripke model and is used to encode the agent's knowledge and the real state of the world. It is defined by a transition function that maps pairs of actions and states into sets of states. We illustrate properties of the action theories, including properties that guarantee finiteness of the set of initial states and their practical implementability. Finally, we relate mA+ to other related formalisms that contribute to RAC in MADs.